There was "absolutely no reason" for cabinet ministers to quit over the issue, he suggested, urging them to "pull behind" Mrs May ahead of a crucial summit of EU leaders on Wednesday.

The current Brexit Secretary, Dominic Raab, went to Brussels on Sunday afternoon to meet with the EU's chief negotiator Michel Barnier ahead of the event.

A Department for Exiting the European Union spokesman said: "With several big issues still to resolve, including the Northern Ireland backstop, it was jointly agreed that face-to-face talks were necessary."

"This is one of the most fundamental decisions that government has taken in modern times," he added.

And Labour, on whom Theresa May may have to rely to win a Parliamentary vote on the deal later this year, said it would not support "any fudge cooked up with Brussels".

"The government are playing chicken on this," Shadow foreign secretary Emily Thornberry told the BBC's Andrew Marr show, claiming a choice between no deal and a "bit of Theresa May nonsense" was unacceptable.

"We say no... We are not agreeing to build half a bridge when we do not know where it is going."

Mr Davis resigned from his post in July - days after Mrs May's so-called Chequers deal was agreed by cabinet - saying he did not believe in the plan.

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Media captionWhat will become of the Irish border when the UK leaves the European Union?

The issue of the border between Northern Ireland and the Republic of Ireland, which will become the UK's border with the EU, is one of the last remaining obstacles to achieving a divorce deal with Brussels.

Wrangling is continuing over the nature of a "backstop" to keep the border open if a wider UK-EU trade arrangement cannot resolve it.

The EU's version, which would see just Northern Ireland remain aligned with Brussels' rules, has been called unacceptable by Mrs May and her Democratic Unionist allies.

Davis's public call to rebellion

That David Davis is no fan of Theresa May's Brexit plan is not surprising.

That he's choosing to ratchet up the pressure with a public call to rebellion aimed at her most senior ministers is perhaps more so.

The former Brexit secretary's own resignation from the cabinet in July did not alter the prime minister's course.

But time to reach a deal with the EU is now considerably shorter, and there have been reports that other senior Conservatives have concerns about the back-up plan for the Irish border too.

The key question is perhaps not so much whom his article might persuade, but whether or not it reflects what some in the cabinet may already be thinking.

Former Tory leader Iain Duncan Smith said it had been a mistake for the prime minister to allow herself to get "boxed in" over the issue of Northern Ireland.

Asked on Sky News' Sophy Ridge show whether he backed calls for a Cabinet rebellion, Mr Duncan Smith said, "when you no longer agree on a fundamental issue, then it's probably time that you found yourself on the back benches".

Negotiations have continued this weekend between the UK and the EU ahead of Wednesday's meeting.

What is the Chequers plan?

At the beginning of the summer the government's senior ministers held a day-long meeting about Brexit at Chequers, the prime minister's official country home in Buckinghamshire.

The aim was to agree what the government wanted from negotiations with the EU about the future relationship between the UK and the EU over Brexit. The plan that emerged from the meeting has become known as the Chequers plan, or sometimes simply Chequers.

The key aim of the plan is to create a free-trade area for goods moving between the EU and the UK while stopping freedom of movement for people between them.

To do this, the UK would commit to collecting import taxes, known as tariffs, on behalf of the EU for goods that arrive in the UK on their way to the EU. Meanwhile, goods that were staying in the UK could be charged at a different rate, depending on any future trade deals the UK agrees with other countries.

The UK would also agree to a "common rulebook" with the EU for manufactured goods and food, which would mean following EU rules and standards. In the future, if the EU changed any of its standards, the UK could decide not to follow those changes but at the risk of losing the free trade agreement for those goods.

The government believes the combination of the common rulebook and collecting tariffs for the EU would avoid the need for checks on goods passing between the UK and the EU, including over the Irish border.

However, the EU doesn't accept all proposals in the Chequers plan. It thinks the proposals amount to "cherry-picking" parts of EU membership - in other words, keeping the bits the UK wants to stay attached to, while rejecting other rules. The EU is also unconvinced the UK would be able to accurately track all the goods moving through it.

The boss of clothing firm Next has suggested leaving the EU without an over-arching deal would not be a disaster for the retail sector and urged ministers to step up their preparations.

Lord Wolfson, a Conservative peer, told Andrew Marr it need not result in delays at the UK's ports as firms could complete new customs declarations online or at their warehouses while tariffs on EU imports could be set at zero to ensure prices do not go up.

But more than three-quarters of NHS trusts have made no preparations for Brexit whatsoever - according to documents obtained by the People's Vote campaign under Freedom of Information requests.

The group also commissioned a YouGov poll of the UK's doctors and nurses, who - according to the poll - now back another referendum by a margin of three to one.